Checking and securing understanding of simultaneous equations | Maths

Starter quiz

Which of these are solutions to the equation $y=3x-4$ ?

$x=0, y=3$

$x=2, y=2$ ✓

$x=5, y=19$

$x=8, y=18$

$x=10, y=26$ ✓
What is the gradient of the line with equation $y=4x+2$ ?

'4' ✓
What is the gradient of the line with equation $2y+5x=10$ ?

2

5

10

$-\frac{2}{5}$

$-\frac{5}{2}$ ✓
What is the $x$ intercept of the line with equation $3y+4x=12$ ?

(0, 3)

(0, 4)

(3, 0) ✓

(4, 0)
Fill in the missing coordinate for the $y$ intercept of the line with equation $3y+4x=12$ (0, ______)

'4' ✓
Which of these shows the line with equation $2y=6-4x$ ?

The __________ shows us a value of $x$ and $y$ that satisfies two linear equations simultaneously when plotted.

gradient

$x$ -intercept

$y$ -intercept

point of intersection ✓
Here are the lines with equations $y=2x+1$ and $y=5-2x$ . What is the solution to both equations simultaneously?

$x=0, y=1$

$x=1, y=3$ ✓

$x=2.5, y=0$

$x=3, y=1$
How many solutions are there to the equations $y=2x+8$ and $y=2x+3$ when solved simultaneously?

none ✓

one

two

infinite
How many solutions are there to the equations $2y=3x+4$ and $4y-6x=8$ when solved simultaneously?

none

one

two

infinite ✓
Here is the line with equation $y=x-1$ . What is the solution to the simultaneous equations $y=x-1$ and $y=2x-4$ ?

$x=0, y=-4$

$x=1, y=0$

$x=2, y=1$

$x=3, y=2$ ✓

$x=4, y=5$
Here is the line with equation $y=x-1$ . What is the solution to the simultaneous equations $y=x-1$ and $3y+2x=12$ ?

$x=0, y=-1$

$x=1, y=0$

$x=2, y=1$

$x=3, y=2$ ✓

$x=4, y=3$

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You can use your knowledge of linear graphs to draw the graphs of both equations on the same axes
If there exists a solution, the point of intersection is that solution
If the lines are parallel then there are no solutions
If the lines lie on top of each other, there are infinitely many solutions

Pupils may mix-up the x and y coordinates.

Remind pupils that the x value is read from the x-axis and is read first. The y value is read from the y-axis and is read second.

Simultaneous equations - Equations which represent different relationships between the same variables are called simultaneous equations.
Linear - The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.